Minimal

Minimal is a term that refers to the smallest or least possible amount or degree. In various fields, it may refer to a minimal element, minimal polynomial, minimal surface, or minimal system, among other concepts.

Mathematics

In mathematics, the term "minimal" is used in a variety of contexts, each with a different meaning.

Minimal element

A minimal element in a set is an element that is not greater than any other element in the set. This concept is used in order theory, a branch of mathematics that studies binary relations.

Minimal polynomial

The minimal polynomial of an algebraic element is the monic polynomial of least degree that has the element as a root. This concept is used in field theory and algebraic number theory.

Minimal surface

A minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature. The concept is used in differential geometry.

Minimal system

A minimal system in dynamical systems theory is a system that is not a proper extension of any other system. This concept is used in the study of topological dynamics.

Computer Science

In computer science, "minimal" can refer to a minimal automaton, which is a deterministic finite automaton such that no proper quotient of it (under the Myhill-Nerode relation) is also a deterministic finite automaton.

Music

In music, "minimal" often refers to minimal music, a style of music that employs limited or minimal musical materials.

See also

• Maximal (disambiguation)
• Minimum
• Minima

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